Question

In a diffraction pattern due to single slit of width 'a', the first minimum is observed at an angle of 30° when the light of wavelength $5400\text{ \AA}$ is incident on the slit. The first secondary maximum is observed at an angle of ($\sin 30^\circ = \frac{1}{2}$)

• A. $\sin^{-1}\left(\frac{3}{4}\right)$
• B. $\sin^{-1}\left(\frac{2}{3}\right)$
• C. $\sin^{-1}\left(\frac{1}{2}\right)$
• D. $\sin^{-1}\left(\frac{1}{4}\right)$

Hint:

Logic Tip: The ratio of the sine of the angles for the 1st maximum to the 1st minimum is simply the ratio of their path differences: $\frac{1.5\lambda}{1.0\lambda} = 1.5$. Thus, $\sin \theta_{max} = 1.5 \times \sin(30^\circ) = 1.5 \times 0.5 = 0.75 = \frac{3}{4}$.

Answer 1

The Correct Option is A